Problem 79 Write \(\sin t\) in terms of \(\... [FREE SOLUTION]

Chapter 4: Problem 79

Write \(\sin t\) in terms of \(\cos t, 0

Short Answer

Expert verified

\(\sin t = \sqrt{1 - \cos^2 t}\) for \(0 < t < \frac{\pi}{2}\)

Step by step solution

Recall the Pythagorean identity

In any right triangle, the Pythagorean theorem tells us that the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides. In terms of sine and cosine, this can be written as: \(\sin^2 t + \cos^2 t = 1\).

Solve for \(\sin t\)

Rewrite the Pythagorean identity to isolate \(\sin t\) on one side: \(\sin^2 t = 1 - \cos^2 t\).

Find the square root on both sides

Taking a square root on both sides, we get \(\sin t = \sqrt{1 - \cos^2 t}\). However, as mentioned prior, since \(0 0\), so the root to be taken is positive.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Write \(\sin t\) in terms of \(\cos t, 0

Short Answer

Step by step solution

Recall the Pythagorean identity

Solve for \(\sin t\)

Find the square root on both sides

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.